Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural...

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Machine Learning in Chemistry

Background:

• Accurate potential-energy hypersurfaces and force fields are crucial for simulating chemical reactions.
• Existing neural network (NN) methods face challenges in simultaneously developing accurate potential energies and their gradients.
• Ab initio molecular dynamics and Monte Carlo simulations require reliable potential energy information.

Purpose of the Study:

• To introduce an improved neural network (NN) approach, Combined Function Derivative Approximation (CFDA), for simultaneous development of potential-energy hypersurfaces and force fields.
• To enhance the accuracy and efficiency of simulations for gas-phase chemical reactions.
• To provide a method that simplifies NN architecture while maintaining high accuracy.

Main Methods:

• The Combined Function Derivative Approximation (CFDA) method trains a single-output NN to represent potential energy, ensuring its derivatives match the potential-energy hypersurface gradient.
• Accurate force fields are computed by differentiating the trained NN output.
• The method allows for weighting of function fitting relative to gradient fitting and can utilize training data from empirical or ab initio methods.

Main Results:

• CFDA training demonstrated superior performance in preventing overfitting, yielding smaller out-of-sample testing errors compared to early stopping and Bayesian regularization across six tested systems.
• The accuracy and interpolation power of CFDA were validated using the H+HBr reaction dynamics, showing superior fits to both potential-energy surfaces and force fields.
• Simulations using the NN potential achieved point-by-point agreement with trajectories on an analytic surface, indicating high fidelity.

Conclusions:

• The CFDA method offers a significant advancement in developing accurate potential-energy hypersurfaces and force fields using neural networks.
• This approach simplifies NN architecture and improves the prevention of overfitting, leading to more reliable simulations.
• CFDA provides a powerful tool for computational chemistry, enabling highly accurate ab initio molecular dynamics and Monte Carlo studies.